F. A. Dudkin, “Irreducible representations of subgroups of finite index in Baumslag–Solitar groups”, Sibirsk. Mat. Zh., 2013, Volume 54, Number 6,Pages <nobr>1273

This article is cited in 4 papers

Irreducible representations of subgroups of finite index in Baumslag–Solitar groups

F. A. Dudkin^ab

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: We describe all finite-dimensional irreducible linear representations over the field of complex numbers for an arbitrary subgroup of finite index of a Baumslag–Solitar group $BS(p,q)=\langle a,t\mid t^{-1}a^pt=a^q\rangle$ for coprime $p$ and $q$. We find necessary and sufficient conditions for the equivalence of these representations, using only standard facts of linear algebra and the description of subgroups of finite index in Baumslag–Solitar groups.

Keywords: Baumslag–Solitar group, irreducible representation, subgroup of finite index.

UDC: 512.543+512.547

Received: 13.06.2012
Revised: 16.11.2012